Question

If A is a square matrix of order 3 such that |adj A| = 64, find |A|.

Answer 1

For any square matrix of order n,
$$\begin{gathered} \left|adjA\right|={\left|A\right|}^{n-1} \\ \Rightarrow 64={\left|A\right|}^2\left[\because \left|adjA\right|=64\right] \\ \Rightarrow \left|A\right|=\pm 8 \end{gathered}$$